3次或4次不可约多项式的分裂域和根式塔

Splitting Fields and Radical Towers for an Irreducible Cubic or Quartic Polynomial

设f(x)是域F上的3次或4次不可约多项式,E是f(x)在F上的分裂域.利用判别式和伽罗瓦理论,给出了E是F的根式塔的一些充分条件和必要条件.

Let f（x） be an irreducible cubic or quartic polynomial over a field F,and suppose that E is a splitting field for f（x） over F.Some sufficient and necessary conditions such that E is a radical tower of F are given by using discriminant and Galois theory.